Motion estimation is critical to many modern signal-processing algorithms. Motion estimation or image registration plays a central role in a broad range of signal processing fields, including, but not limited to RADAR, SONAR, light microscopy and medical imaging. In medical ultrasound, a few well-known applications include extended field of view imaging, estimation of blood and tissue motion, and estimation of radiation force or mechanically induced displacements for elasticity imaging. Because of its central significance, estimator accuracy, precision, and computational cost are of critical importance to these and numerous other applications. The effort spent in this area is reflected in the variety of algorithms that have been developed.
While cross-correlation and similar pattern matching techniques developed for continuous signals can be readily applied to sampled, real-world data, these approaches are limited to motion estimates that are multiples of the sample distance. Various strategies have been developed in an attempt to circumvent this limitation. One approach is to interpolate the raw sampled data to a finer sampling rate. Unfortunately this approach retains the same problem, albeit at a smaller sample size. Further, this dramatically increases the computational cost of motion tracking.
Another strategy is to interpolate the pattern-matching grid, either at a higher sampling rate, or using an analytical function. This approach typically retains a high bias. Another widely referenced approach is the “grid slopes” algorithm as referred to in Geiman et al., in “A Comparison of Algorithms for Tracking Sub-pixel Speckle Motion”, IEEE Ultrasonic Symposium, pp. 1239-1242, 1997 and Bohs et al. in “Ensemble Tracking for 2D Vector Velocity Measurement: Experimental and Initial clinical Results”, IEEE Trans. Ultrason., Ferroelect., Freq. cont., vol. 45, no. 4, pp. 912-924, 1998.
Each of these algorithms can be applied to reduce systematic errors in motion estimation, however each entails an increased computational cost and significant bias errors. Spline-based image registration has also been described in the literature, however published techniques are limited by the use of a separable spline model, and by a lack of quantification of intrinsic bias errors, e.g., see Thevanez et al., “A Pyramid Approach to Subpixel Registration Based on Intensity”, IEEE Transactions on Image Processing, vol. 7, pp. 27-41, 1998.
Viola et al., “A Novel Spline-Based Algorithm for Continuous Time-Delay Estimation Using Sampled Data”, IEEE. Trans. Ultrasonics Ferroelectrics & Frequency Control, Vol. 52, pp. 80-93, 2005, which is incorporated herein, in its entirety, by reference thereto, describes a one-dimensional displacement estimator, but not a multidimensional estimator. Although Viola et al. indicates that it is generally straight-forward, the straight-forward approach requires solving a very large number of simultaneous equations, which is too costly in terms of the memory and computing power required, to be practically useful in most applications.
It has been shown that the performance of tissue elasticity imaging can be significantly improved by the application of 2D companding, but the computational burden of this technique has limited its application.
There is a continuing need for methods, systems and algorithms for motion estimation applications that provide precise estimation of sub-sample displacements without undue computational cost. The present invention provides solutions that can produce estimation of multi-dimensional sub-sample displacements that have a better precision and accuracy than currently existing methods. Furthermore, it would be desirable to estimate more complex deformations with better precision and accuracy.
Systems, methods and algorithms capable of calculating displacement estimates having errors that are less than the distance between two consecutive samples and less than those of existing algorithms would also be desirable.